Turbomachinery Design Considerations

EGR 4347 Analysis and Design of Propulsion Systems

Euler Pump Equation

titeiieec

c hhmvrvrg

mW

..

.

Compressor Axial Schematic

Compressor Centrifugal Schematic

Compressor Typical Velocity Diagram

Compressor Repeating Row Nomenclature

Airfoil Pressure and Velocity

Important Parameters

• Compressor Efficiency, c

• Stage Efficiency, s

• Polytropic Efficiency, ec

• Stage Pressure Ratio, s

• Overall Pressure Ratio, c

Degree of Reaction

• Desirable value around 0.513

12

hh

hh

riseenthalpystaticstage

riseenthalpystaticrotorRco

Diffusion Factor

• Quantifies the correlation between total pressure loss and deceleration (diffusion) on the upper (suction) surface of blade (rotor and stator)

is the solidity – the ratio of airfoil chord to spacing

i

ei

i

e

avg

e

V

vv

V

VDasdefine

V

VVD

21max

Diffusion Factor Data

Hub, Mean, and Tip Velocity Diagrams

Stall and Surge

Parameters Affecting Turbine Blade Design

Vibration Environment

Tip Shroud

Inlet Temperature

Blade Cooling

Material

Number of Blades

Airfoil Shape

Trailing-Edge Thickness

Allowable Stress Levels (AN2)(N = Speed, RPM)

Service Life Requirements

Turbine Prelim Design Focuses on Defining a ‘Flowpath’ that Meets Customer Requirements

Customer Req’ts/Desires

Performance Mission Cost & Risk

FN, SFC Req’tsAero Technology

Life Req’ts Mech. &Cooling Technologies

PerformanceCycle Design Combustor

Design

MaterialSelections

TurbineAero Design

Manufacturing

ComponentTemp to other

areas

Preliminary Design = “Frozen” Turbine Flowpath

TurbineMech Design

AN2

rh

Wc

Clearance

NoNo

Yes Meet Requirements

Turbine Mechanical Detailed Design

• Detailed Design Accomplishes Two Functions:– Verify Assumptions/Choices Made in Preliminary Design

– Provide Detailed Geometry Required to Achieve Preliminary Design Goals

• Detail Mechanical Design Disciplines:– Materials Selection - satisfy life/performance goals

– Secondary Flow Analysis - define/control nonflowpath air (e.g. cooling)

– Heat Transfer - component temperature definition

– Stress Analysis - component stresses

– Vibration Analysis - design to avoid natural frequencies

– Life Analysis - define component life for all failure modes

Turbine Nomenclature

50% Reaction Turbine

0% Reaction or Impulse Turbine

Hub, Mean and Tip Velocity Diagrams

Velocity Triangles

1

V 1

rr

V 2

V 2 R

u 2

v 2V 2

2

2

1 2 3

3

rV 3 R

V 3

3

V 3 R

u 3

v3 R = v 3 + r

“ABSOLUTE” FLOW ANGLES

tan

tan

22

2

33

3

v

u

v

u

“RELATIVE” BLADE ANGLES

tan

tan

22

2

2

2

33

3

3

3

v

u

v r

u

v

u

v r

u

R

R

Relating ’s and ’s

v u r u

v u r u2 2 2 2 2

3 3 3 3 3

tan tan

tan tan

tan tan tan tan 2

3

23 2

3

23

u

u

u

u

TURBINE ANALYSIS – Velocity Triangles

TURBINE ANALYSIS

• Euler Turbine Equation:

Torquemg

r v r v

Wm

gr v r v mc T T

ci i e e

tc

i i e e p ti te

v2V2

u2

inlet, i

v3 u3

exit, e

V3convention:

v3 = -ve

also, ri = re= r

rg

v v c T Tc

p t t2 3 2 3

TURBINE ANALYSIS• Turbine Efficiency:

– Adiabatic (Isentropic)

– Polytropic

• Stage Loading Coefficient, :

– Typical values: 1.3 - 2.2

ts

st t

1

1 1

s s

et t t 1

Stage work / mass

(Rotor Speed)2g h

rc t

2

TURBINE ANALYSIS

axial velocity entering rotor

rotor speedu

r2

• Flow Coefficient, : Typical values 0.5 - 1.1

• Degree of Reaction, °R:

– °Rt = 0 Impulse turbine

– Reaction turbine

Rh hh h

T TT Tt

t t t t

enthalpy rise in rotortotal enthalpy rise for stage

2 3

1 3

2 3

1 3

Rt 0

• Pressure Loss Coefficient, t:

• Velocity Ratio, VR: Typical values: 0.5 - 0.6

tti te

te e

P P

P P

VR

VRr

g hc t

rotor speedvel equivalent of the change in total enthalpy

2

12

TURBINE ANALYSIS

Tip Leakage

Profile Loss

Endwall Loss

Cooling Loss

Turbine Mechanical Design

• AN2: Rotor Exit Annulus Area x [Max Physical Speed]2

– Units: in2 x RPM2 x 1010, typical values: 0.5<AN2<10 x1010

– Typical Limits:

• Cooled Blade < 5 x 1010

• Advanced Technology < 6.5 x 1010

• Uncooled Solid Blade < 10 x 1010

• LPT < 7 x 1010

– Use max physical speed; not design point or TO speed

– Blade Airfoil Stress is Primarily Driven by AN2

– Blade Pull Load Driven by AN2

Turbine Mechanical Design – Hub and Tip Speed Limits

• rh2: Hub radius x 2/60 x Max Physical RPM– Units: ft/s

– Typical Values:

• HPT - 1000 ft/s < rh2 < 1500 ft/s

• LPT - 500 ft/s < rh2 < 1000 ft/s

– Use max physical RPM; not design point or TO speed

– Disk Stress is Driven Primarily by rh2

– Disk and Blade Attachment Stresses are a function of rh2 and AN2

Structures

- Rotational Stress (Centrifugal Stress)- Bending Stress due to the lift of “airfoils”- Buffet/Vibrational Stress- Flutter due to resonant response- Torsion from shaft torque- Thermal Stress due to temperature gradients- FOD- Erosion, Corrosion, and Creep

Structures

Structures

Structures - Stress Calculations

- Rotational Stress (Centrifugal Stress)-- Same as for compressor, c, blade

- Disk Thermal Stress, t

-- assume T = T(r) = T0 + T(r/rH)-- - coef of linear thermal expansion-- E - Modulus of Elasticity 0 rH

T

T0

T+T

r

rH

Disk

r

Htr r

rTE1

3

Ht r

rTE21

3

radial stress

tangential stress